This invention relates to heat transfer tubes and particularly to tubes which have increased internal surface area as compared to plain tube. U.S. Pat. Nos. 2,960,114 and 3,696,863 each disclose a composite assembly comprising a tube and an externally ribbed or finned insert core and discuss the desirability of providing such a core for enhancing the internal heat transfer coefficient of a tube in certain refrigeration applications. The earlier of the aforesaid patents teaches the locking of the inside tube wall and the fins on the core in tight mechanical relationship by means of longitudinal flutes formed in the smooth external pipe surface in the region between adjacent pairs of internal fins. The later patent teaches that a ribbed or finned insert core can be placed inside an outer tube which has been previously externally finned. The core is then mechanically bonded to the previously finned outer tube by grooving the annular, transversely arranged external fins in a general longitudinal direction at a plurality of locations around the circumference of the tube. The grooving serves to divide each annular fin into a plurality of separate fins in a common plane.